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DSimon comments on Human errors, human values - Less Wrong
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Another similar problem that I've encountered runs thus: suppose we're in a scenario where it's one person's life against a million, or a billion, or all the people in the world. Suppose aliens are invading and will leave Earth be if we were to kill an arbitrarily-determined innocent bystander. Otherwise, they will choose an arbitrary person, take him to safety, and destroy Earth, along with everyone else. In that case, consensus seems to be that the lives of everyone on Earth far outweigh a healthy innocent's rights.
The largest difference between the two cases is numbers: five people becomes six billion. If there is another difference, I have yet to find it. But if it is simply a difference in numbers, then whatever justification people use to choose the healthy man over five patients ought to apply here as well.
At a practical level, there's another significant difference between the two cases: confidence in the probabilities.
As has been pointed out above, the thought experiment with the donors has a lot of utilitarian implications that are farther out than just the lives of the five people in the doctor's room. Changing the behavior of doctors will change the behavior of others, since they will anticipate different things happening when they interact with doctors.
On the other hand, we haven't got much basis for predicting how choosing one of the two scenarios will influence the aliens, or even thinking that they'll come back.